@cite{beavers-2010} The Structure of Lexical Meaning: Why Semantics Really Matters #
Argument realization in direct/oblique alternations is governed not by event structure but by strength of truth conditions. Direct realization encodes monotonically stronger truth conditions than oblique realization. This is captured by:
An affectedness hierarchy — four degrees of change, each an existential weakening of the last: quantized ⊃ nonquantized ⊃ potential ⊃ unspecified.
L-thematic roles — sets of implicationally related entailments. The three affectedness entailments produce a structured subset hierarchy with exactly 4 semantically non-vacuous roles (of 8 possible).
The Morphosyntactic Alignment Principle (MAP) — when an argument alternates between direct and oblique realization, the direct variant bears L-thematic role R and the oblique bears Q ⊆_M R (minimal weakening).
Deepest theorem #
MAP_holds_all_alternations: for every attested object/oblique alternation
in the data, the direct-argument affectedness degree is ≥ the oblique's.
This connects the mathematical structure of the hierarchy (derived from
truth-conditional definitions) to empirical argument realization facts
through the MAP.
An L-thematic role for patienthood is a set of affectedness entailments. Beavers reduces Dowty's 5 P-Patient entailments to 3 implicationally related ones.
The three entailments:
quantized: x undergoes a QUANTIZED changenonquantized: x undergoes a NONQUANTIZED changepotential: x has POTENTIAL for a change
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- Phenomena.ArgumentStructure.Studies.Beavers2010.instBEqPatientLRole.beq x✝¹ x✝ = false
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An L-role is valid iff it respects the implicational constraints: quantized → nonquantized → potential.
This rules out 4 of the 8 possible combinations:
- {q} alone: q → nq violated
- {q, p} without nq: q → nq violated
- {q, nq} without p: nq → p violated
- {nq} alone: nq → p violated
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The four valid L-thematic roles.
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Key theorem: exactly 4 of 8 combinations are valid. The implicational relationships between entailments constrain the space of semantically contentful L-thematic roles.
Subset ordering on L-thematic roles: R₁ ⊆ R₂ iff every entailment in R₁ is also in R₂.
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Strict subset: ⊂
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The four valid roles form a linear chain under ⊂: {} ⊂ {p} ⊂ {nq,p} ⊂ {q,nq,p}
The hierarchy is linear: no incomparable pairs among valid roles.
Minimal contrast: Q ⊆_M R iff Q = R or Q ⊂ R with no intervening valid role P such that Q ⊂ P ⊂ R.
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The attested minimal contrasts are exactly the adjacent pairs.
Skipping a level is NOT a minimal contrast.
The affectedness degree corresponding to a valid L-thematic role.
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The MAP: when participant x may be realized as either a direct argument (bearing L-thematic role R) or an oblique (bearing role Q), Q ⊆_M R — the oblique role is a minimal weakening of the direct role.
Equivalently: the direct object's affectedness degree is ≥ the oblique's.
This is a prominence-preservation principle: stronger truth conditions map to more prominent morphosyntactic realization.
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- Phenomena.ArgumentStructure.Studies.Beavers2010.MAP directRole obliqueRole = obliqueRole.subset directRole
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An observed alternation contrast: a verb with its direct-object and oblique affectedness degrees.
- verb : String
- alternationType : DiathesisAlternation
- directDegree : Semantics.Lexical.Verb.Affectedness.AffectednessDegree
- obliqueDegree : Semantics.Lexical.Verb.Affectedness.AffectednessDegree
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- Phenomena.ArgumentStructure.Studies.Beavers2010.instBEqAlternationContrast.beq x✝¹ x✝ = false
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eat conative: "ate the pizza" (quantized) vs "ate at the pizza" (nonquantized). The object variant entails total consumption; the oblique entails only some consumption occurred.
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cut conative: "cut the rope" (nonquantized) vs "cut at the rope" (potential). The object variant entails some damage; the oblique entails only that damage was possible (contact under modality).
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hit conative: "hit the rope" (potential) vs "hit at the rope" (unspecified). The object variant entails potential for change (if contact, then possible result); the oblique entails only potential contact under double modality.
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load locative (location as object): "loaded the wagon" (quantized) vs "loaded hay onto the wagon" — the wagon undergoes quantized change (completely filled), the hay undergoes nonquantized change (moved).
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load locative (theme as object): "loaded the hay" (quantized) vs "loaded the wagon with the hay" — the hay undergoes quantized change (all moved), the wagon undergoes nonquantized change.
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cut/slice locative (location as object): "cut the window with the diamond" (nonquantized) vs "cut the diamond on the window" — both undergo potential change, but the object has nonquantized.
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cut/slice locative (theme as object): same contrast.
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All attested alternation contrasts.
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MAP holds for a single contrast: direct ≥ oblique.
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The deepest theorem: the MAP holds for ALL attested alternation contrasts. Every direct realization has truth conditions at least as strong as the corresponding oblique realization.
This connects:
- The mathematical structure of the affectedness hierarchy (§1–2)
- The MAP as a prominence-preservation principle (§3)
- The empirical alternation data (§4)
Any change to the affectedness assignments breaks this theorem.
Each conative contrast is exactly a minimal contrast — adjacent levels on the hierarchy. This is not stipulated; it follows from the verbs' truth conditions.
The three conatives tile the entire hierarchy — every adjacent pair appears exactly once. Together they demonstrate the full implicational chain.
The MAP rules out "impossible" alternations where the oblique would have more entailments than the direct object.
Example: a hypothetical alternation where the DO is POTENTIAL but the oblique is QUANTIZED is ruled out — it would mean the less prominent realization has stronger truth conditions.
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Bridge to existing alternation data: the conative alternation
data for eat, cut, and hit in Data.lean records .participates,
confirming these alternations are attested.
Bridge to existing alternation data: break does NOT participate in the conative. This is predicted: break objects undergo quantized change (CoS), and the conative would weaken to nonquantized — but break's meaning inherently requires a specific result state, so the weakening is blocked by the verb's lexical semantics.
Bridge to existing alternation data: locative alternation is attested for spray/load verbs.
The profileToDegree bridge (formerly §8) and its verification theorems
have been promoted to Theories/Semantics/Events/Affectedness.lean.
They are opened at the top of this file.
@cite{beavers-2010} argues that the MAP and event decompositions are complementary, not competing (the paper's conclusion, §6):
| Approach | Semantics | Morphosyntax |
|-----------------|----------------------------------|--------------------------|
| Decompositions | gross causal/temporal structure | subject/nonsubject |
| MAP | fine-grained lexical entailments | direct/oblique |
The existing `EntailmentProfile` captures the gross agentivity structure
(P-Agent features → subject selection). Beavers 2010 adds the missing
piece: fine-grained P-Patient structure → direct/oblique alternations.
Subject selection (from @cite{dowty-1991}) and object alternations (from @cite{beavers-2010}) are independent principles operating on different argument positions. The ASP governs subjects; the MAP governs direct vs. oblique objects.
@cite{grimm-2011}'s PersistenceLevel reformulates P-Patient as 4
persistence dimensions (existential/qualitative × beginning/end).
Beavers' affectedness hierarchy maps systematically onto this lattice:
| Beavers degree | Grimm persistence | Interpretation |
|------------------|----------------------|-----------------------------|
| quantized | exPersEnd | Entity created/consumed |
| | quPersBeginning | Entity changed to specific |
| nonquantized | quPersBeginning | Entity changed (nonspecific)|
| potential | totalPersistence | Entity may change |
| unspecified | totalPersistence | No change entailment |
The mapping is not injective: both `quantized` and `nonquantized` can
map to `quPersBeginning` (the entity changes but persists). The
distinction between them is about *specificity of the result state*,
which Grimm's persistence dimensions don't capture — it's a property
of the scale, not of persistence. This is where the theories are
genuinely complementary.
Map affectedness degrees to their most typical persistence level. This captures the systematic correspondence; edge cases (creation verbs mapping to exPersEnd for quantized) require verb-specific information.
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The two Grimm levels that correspond to "affected" roles (quPersBeginning = changed, exPersEnd = created/destroyed) are both ranked lower than totalPersistence on Grimm's lattice. Lower persistence = higher affectedness. This is the Grimm-Beavers convergence.
Bridge: kick object has persistence quPersBeginning (changed but persists) and affectedness nonquantized — both theories agree it's affected but not to a specific degree.
Bridge: build object has persistence exPersEnd (created) and affectedness quantized — both theories agree on maximal patient status.
Bridge: eat object has persistence exPersBeginning (consumed) and affectedness quantized — both theories agree on maximal change.
The deepest cross-theory result: Grimm's persistence ordering and Beavers' affectedness ordering are monotonically related for canonical verb profiles. Arguments with higher affectedness (Beavers) have lower persistence (Grimm). They formalize the same intuition — degree of change — from complementary perspectives.